In many computer vision applications, images can be processed to detect objects, or to improve the quality of the input images by, e.g., background subtraction, removing or reducing unwanted artifacts, noise and occlusions. In image processing, principal component analysis (PCA) is commonly applied for dimensionality reduction. However, when the image data contains unintended artifacts, such as gross corruptions, occlusions or outliers, the conventional PCA can fail. To solve this problem, robust PCA (RPCA) models can be used.
An online recursive RPCA can separate data samples in an online mode, i.e., with only a previous estimate and newly acquired data. Unlike the conventional RPCA methods, which first saves all the data samples and then processes them, the online RPCA significantly reduces the required memory requirement and improves computational efficiency and convergence.
For multidimensional data (tensors) of order greater than 2, it is common to embed the data into a vector space by vectorizing the data such that conventional matrix-based approaches can still be used. Although this vectorization process works well in most cases, it restricts the effectiveness of the tensor representation in extracting information from the multidimensional perspective.
Alternatively, tensor algebraic approaches exhibit significant advantages in preserving multidimensional information when dealing with high order data. However, it is very time-consuming for the tensor RPCA to operate in batch mode because all of the high dimensional data needs to be stored and processed.